What should I do with the weights in the shed?

Level 1:

Recognize these things from anywhere else?

Level 2:

If you use a little bit of your imagination, the hemisphere looks
somewhat like the platform-side of the orangish brown ball outside.

Level 3:

The hemisphere is an uncompleted counterweight for the lever.
The blocks are weights that can be moved onto the hemisphere to create a heavier counterweight.
If you found other weights like these in J'nanin, this puzzle will be a lot easier. If you
didn't, you can either use trial and error or go back to J'nanin using the linking book located
close to the "entrance" to the Age.